Jennifer, I'm confused about what you're trying to do and the type of bags you are using - are they the 'soft' plastic like Target store bags or more crinkly like Walmart bags? Or are they paper merchandise bags?
What type of machine do you have?
I've *never* sewn with paper or plastic on my machine, I've been afraid of damaging needles, gears, and other mechanics of the machine. I do have a friend though who likes to use fancy stitches on paper for her scrapbooking and she uses an old 1940's metal monstrosity of a Kenmore, a model that is virtually indestructable. Her paper through is thinner, and she uses sets aside needles just for that.